4 citations · 7 across the 3 of their papers we have counts for
4 papers
On Yoccoz Return Functions
Nathaniel D. Emerson
We study the dynamics of complex polynomials. We obtain results on Poincare return maps defined on certain neighborhoods of a point with bounded orbit under a polynomial. We introd…
Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets
Nathaniel D. Emerson
We consider the harmonic measure on a disconnected polynomial Julia set in terms of Brownian motion. We show that the harmonic measure of any connected component of such a Julia se…
A family of meta-Fibonacci sequences defined by variable order recursions
Nathaniel D. Emerson
We define a family of meta-Fibonacci sequences where the order of the of recursion at stage n is a variable r(n), and the n^{th} term of a sequence is the sum of the previous r(n)…
Return times of polynomials as meta-Fibonacci numbers
Nathaniel D. Emerson
We consider generalized closest return times of a complex polynomial of degree at least two. Most previous studies on this subject have focused on the properties of polynomials wit…